App icons are part of the application and not something easily changed by the user.
Changing the icon will change the data the application hashses over for its signature and so some things will complain the application is corrupt.
Icons can be changed by going to the Application in Finder and then choose Show Package Contents. In the simplest case an icon file will usually be for application X (I think the developer can decide to use another name)
X.app/Contents/Resources/X.icns You can then replace that file. However if the application is well written and so complies with Apple's Human Interface Guidelines there will be several icons
Every app must include several sizes of its app icon for display in the Finder, Dock, Launchpad, and elsewhere.
Note that when Homebrew gets an updated version of Emacs and you update it will overwrite the change you made.